二叉搜索树BinarySearchTree的实现

这里因为删除节点的函数写得不错，所以代码放上来保存一下，这个函数当然不是我写的。//BTNode.h#ifndef BTNODE_H#define BTNODE_H#include <cstdio>typedef int datatype;typedef struct BTNode{datatype data;BTNode* left;BTNode* right;BTNode* father;datatype val;BTNode(datatype dataPara,datatype valPara = NULL):data(dataPara),left(NULL),right(NULL), val(valPara), father(NULL){};}*nodePtr;#endif//BST.h#ifndef BST_H#define BST_H#include "BTNode.h"#include <iostream>using namespace std;class BST //means Binary Search Tree{public:BST() :rootPtr(new BTNode(0)){};~BST();void Insert(datatype data);void Delete(datatype data);void count(datatype data);void find(datatype data);void Clear(datatype data);void InRerverse(const nodePtr &node);void Rerverse();private:nodePtr rootPtr;void InsertHelp(datatype data, nodePtr &node);void DeleteHelp(datatype data, nodePtr &node);nodePtr findMin(nodePtr node);};#endif//BST.cpp#include "BST.h"BST::~BST(){}void BST::Insert(datatype data){InsertHelp(data, rootPtr->left);}void BST::InsertHelp(datatype data, nodePtr &node){if (node != NULL){if (data == node->data)cout << "the val has exist in the tree!" << endl;else if (data < node->data)InsertHelp(data, node->left);elseInsertHelp(data, node->right);}elsenode = new BTNode(data);}void BST::InRerverse(const nodePtr &node){if (node != NULL){InRerverse(node->left);cout << node->data << " ";InRerverse(node->right);}}void BST::Rerverse(){InRerverse(rootPtr->left);}void BST::Delete(datatype data){DeleteHelp(data, rootPtr->left);}void BST::DeleteHelp(datatype data, nodePtr &node){if (node != NULL){if (node->data < data)DeleteHelp(data, node->right);else if (node->data > data)DeleteHelp(data, node->left);else if (node->left != NULL && node->right != NULL){node->data = findMin(node->right)->data; //这里没有调用找后继节点的函数，因为找后继节点是分情况讨论的，而这里不需要分情况DeleteHelp(data, node->right); //只需要找到沿路径的最小值就可以了}else{nodePtr temp = node;node = (node->left == NULL) ? node->right : node->left;delete temp;}}

}

nodePtr BST::findMin(nodePtr node){while (node != NULL || node->left != NULL){node = node->left;}return node;}

//Main.cpp 其实就是测试代码#include "BST.h"int main(){BST A;A.Insert(3);A.Insert(4);A.Insert(1);A.Insert(2);A.Insert(6);A.Insert(5);A.Insert(0);A.Insert(7);A.Insert(9);A.Insert(8);A.Insert(0);A.Delete(0);A.Delete(7);A.Rerverse();}这里来一版可以查找前驱/后继节点的，这时候node的结构体里面必须包括父节点的信息~，insert/delete等函数也要调整父节点信息

void BST::Insert1(datatype data)
{
InsertHelp1(data, rootPtr->left, rootPtr);
}

void BST::InsertHelp1(datatype data, nodePtr &node, nodePtr &father){if (node != NULL){if (data == node->data)cout << "the val has exist in the tree!" << endl;else if (data < node->data)InsertHelp1(data, node->left, node);elseInsertHelp1(data, node->right, node);}else{node = new BTNode(data);node->father = father;}}

void BST::Delete1(datatype data){DeleteHelp1(data, rootPtr->left);}

void BST::DeleteHelp1(datatype data, nodePtr &node){if (node != NULL){if (node->data < data)DeleteHelp1(data, node->right);else if (node->data > data)DeleteHelp1(data, node->left);else if (node->left != NULL && node->right != NULL){node->data = findMin(node->right)->data; //这里没有调用找后继节点的函数，因为找后继节点是分情况讨论的，而这里不需要分情况DeleteHelp1(data, node->right); //只需要找到沿路径的最小值就可以了}else{nodePtr temp = node;node = (node->left == NULL) ? node->right : node->left;if (node != NULL)node->father = temp->father; //判定node是否为空delete temp;}}}

 

nodePtr BST::findMin(nodePtr node){while (node != NULL && node->left != NULL){node = node->left;}return node;}

</pre><pre class="cpp" name="code">然后是真正的找后继节点的函数，形参是一个nodePtr,返回也是一个nodePtr

</pre><pre class="cpp" name="code">nodePtr BST::findPost(nodePtr node){if (node != NULL){if (node->right != NULL){return findMin(node->right);}else{while (node->father != rootPtr && node == node->father->right)node = node->father;return node->father;}}elsereturn NULL;//return NULL;}

也可以做得高端一点，输入一个Data返回他的后继节点，只需要多写个找data对应的node的函数

nodePtr BST::findNode(datatype data){return findNodeHelp(data, rootPtr->left);}nodePtr BST::findNodeHelp(datatype data, nodePtr node){if (node != NULL){if (data > node->data)return findNodeHelp(data, node->right);else if (data < node->data)return findNodeHelp(data, node->left);elsereturn node;}elsereturn NULL;}

最后是测试函数：

#include "BST.h"int main(){BST A;A.Insert1(3);A.Insert1(4);A.Insert1(1);A.Insert1(2);A.Insert1(6);A.Insert1(5);A.Insert1(0);A.Insert1(7);A.Insert1(9);A.Insert1(8);A.Insert1(0);A.Delete1(0);A.Delete1(7);cout << A.findPost(A.findNode(6))->data << endl;A.Rerverse();}

代码已经跑过啦，没问题~,二叉搜索树就这些了